To make the link with the corrupted setting from Definiton REF , remark that if an adversary chose \(\lfloor (1-\varepsilon )n\rfloor \)  inliers i.i.d from \(P\)  and \(\lceil \varepsilon n\rceil \)  outliers i.i.d from \(Q\) , then the resulting empirical distribution converges to \(P_\varepsilon \)  and by continuity of \(T\)  with respect to the weak topology (see Hampel's theorem in [1]}), we have that \(T(X_1^n) \rightarrow T(P_\varepsilon )\) .
